Incorporating Power Electronic Converters Reliability into Modern Power System Reliability Analysis

Incorporating Power Electronic Converters Reliability into Modern Power System

Reliability Analysis

Peyghami, Saeed; Blaabjerg, Frede; Palensky, Peter DOI

10.1109/JESTPE.2020.2967216 Publication date

2021

Document Version

Accepted author manuscript Published in

IEEE Journal of Emerging and Selected Topics in Power Electronics

Citation (APA)

Peyghami, S., Blaabjerg, F., & Palensky, P. (2021). Incorporating Power Electronic Converters Reliability into Modern Power System Reliability Analysis. IEEE Journal of Emerging and Selected Topics in Power Electronics, 9(2), 1668-1681. [8962198]. https://doi.org/10.1109/JESTPE.2020.2967216

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Abstract— This paper aims to incorporate the reliability model of power electronic converters into power system reliability analysis. The converter reliability has widely been explored in device- and converter-levels according to physics of failure analysis. However, optimal decision-makings for design, planning, operation and maintenance of power electronic converters require system-level reliability modeling of power electronic-based power systems. Therefore, this paper proposes a procedure to evaluate the reliability of power electronic based power systems from the device-level up to the system-level. Furthermore, the impact of converter failure rates including random chance and wear-out failures on power system performance in different applications such as wind turbine and electronic transmission lines is illustrated. Moreover, due to a high calculation burden raised by the physics of failure analysis for large scale power electronic systems, this paper explores the required accuracy for reliability modeling of converters in different applications. Numerical case studies are provided employing modified versions of the Roy Billinton Test System (RBTS). The analysis shows the converter failures may affect the overall system performance depending on its application. Therefore, an accurate converter reliability model is, in some cases, required for reliability assessment and management in modern power systems.

Index Terms—reliability, wind farm reliability, wear-out failure, converter reliability, adequacy, HVDC reliability.

I. I

NTRODUCTION

Electric power system modernization is essential for reliable and secure power delivery with low to zero carbon footprint. It requires deploying new technologies and infrastructure as well as deregulating the electricity sector. Some stablished technologies have a considerable role in power systems modernization including renewable energy resources, storages, electronic transmission and distribution systems, and e-mobility. Notably, power electronics plays an underpinning role in energy conversion process of aforementioned technologies [1]. Particularly, moving toward one hundred percent renewable energies has intensified the importance of power electronics in future power systems. However, power converters are one of the frequent source of failures in many applications [2]–[4], hence introducing high downtime and maintenance costs [2]–[11] Moreover, according to field data and industrial experiences, the power converters are exposed to aging and wear-out failures depending on the operating conditions [3]–[5], [12], [13].

A power converter is made up of various sub-systems including power modules, capacitors, gate drivers, control units, and cooling system. Electrolytic capacitors and power modules are the two most fragile components which are also prone to wear-out failure. The reliability of these components

depends on different factors such as device mechanical strength, applied electrical load, climate conditions, control and switching schemes. These factors cause degradation of component materials during long-term operation of the conver-ter, finally triggering potential failure mechanisms. Physics of failure-based Stress-Strength Analysis (SSA) for different failure mechanisms can be used for component reliability prediction and enhancement from wear-out standpoint.

The SSA requires electro-thermal modeling in three hierarchical levels including device-level, converter-level and system-level [14]. The system-level modeling identifies the loading of the converter according to its application in the power system. For instance, the loading of parallel-connected converters depends on power sharing strategies. Moreover, the converter-level studies include the electrical domain modeling and simulations in order to find out the stress of each components under applied control and switching strategies. Finally, the device-level analysis requires electro-thermal modeling of devices for obtaining key thermal variables, such as hot-spot temperature, which are enabling failure mechanisms under a given mission profile. As a result, the SSA analysis comprise very fast dynamics in the range of switching frequency at the device-level to the slow dynamics in the range of hourly load changes at the system-level. Therefore, the wear-out failure prediction over an annual mission profile is a time-consuming process. In the system-level analysis it will introduce very high calculation burden especially in large-scale power systems.

So far, the SSA has been employed in device-level for lifetime modeling and extension in capacitors and semiconductor devices [12], [15]–[19]. In the converter-level, the SSA is used for converter lifetime extension by active thermal management approaches such as appropriate modulation strategies [20]–[22], adaptive switching frequency [23], and active/reactive power control [24]–[26]. The converter topologies and photovoltaic array characteristics are other factors affecting the converter lifetime [22], [27], [28]. Furthermore, the capacitors lifetime expansion is explored in [27], [28] by interleaving the converters. Moreover, the system-level reliability enhancement in multi converter systems is performed by appropriately modifying the converters loading and shifting the device damages from high-stressed converter to the low-stressed one [14], [29].

The aforementioned reliability analyses in [11], [14], [23]– [29], [15]–[22] are limited to the converter lifetime prediction and enhancement even at the system-level studies. However, optimal decision-making in design, planning, operation and maintenance of the converters in the power systems requires to analyze their impacts on power system reliability. This requires bridging the power electronic reliability concepts and the power system reliability assessment approaches.

Incorporating Power Electronic Converters Reliability

into Modern Power System Reliability Analysis

Saeed Peyghami, Member, IEEE, Frede Blaabjerg, Fellow, IEEE, Peter Palensky, Senior Member, IEEE

This work was supported by the Reliable Power Electronic-Based Power System (REPEPS) project at the Department of Energy Technology, Aalborg University as a part of the Villum Investigator Program funded by the Villum Foundation.

The power system reliability is defined as a measure of its ability to cope with customer demands [30]. Technically, this ability is measured by adequacy indices such as Loss OF Load Expectation (LOLE) and Expected Energy Not Supplied (EENS) [30]. Besides the conventional power systems reliability analysis [30], the reliability of power electronic-based power systems such as Wind Farms (WFs) and High Voltage Direct Current (HVDC) transmission systems have been widely studied, e.g., in [30], [31], [40]–[42], [32]–[39]. Moreover, the reliability of microgrid systems considering the impact of power electronic converters has been explored in [31]. In the state-of-the-art research [30], [31], [40]–[42], [32]– [39], the failure rate of converters in power system analysis is obtained from the historical data of similar cases. Moreover, the wear-out failure of converters has not been taken into account in the power system reliability assessment. In practice, the wear-out of converter components may happen earlier than the expected lifetime [12]. Therefore, not only the failure rate of converter during operation will be increased, but also its end-of-life will be limited. Hence, the converter components aging will affect the overall system reliability and risk, consequently inducing higher downtime and maintenance costs especially in the large-scale power electronic-based power systems.

In order to avoid these issues, appropriate strategies must be adopted for optimal decision-making in planning, operation and maintenance of modern power electronic-based systems. This requires system-level reliability analysis by incorporating the converter reliability modeling in power system reliability assessment. This procedure is very time-consuming, and in practice, for large-scale power systems is almost impossible. This is due to the fact that the electro-thermal modeling based on SSA requires time-domain analysis with the time frame of interest from microsecond associated to the converter switching frequency up to the hourly load variations. Therefore, system-level reliability modeling in power electronic-based systems needs simplified electro-thermal modeling techniques in different time frames.

According to the aforementioned issues posed by proliferation of converters in power systems, this paper aims to address the following challenges:

1) Since any decision-making regarding converters operation, planning and maintenance must be performed at the system-level, hence, the system-level reliability modeling in power electronic-based systems is of high importance. This paper aims at bridging the converter reliability models and power system reliability concepts for evaluating the reliability of power electronic-based power systems.

2) Due to the increasing use of converters in power systems, their failure rates associated with the random chance and wear-out failures may affect the overall performance of power systems. This paper will illustrate the impact of converter failures and aging on the power system reliability.

3) Due to the complexity of the reliability modeling in converters based on SSA, the simplified approaches should be introduced for system-level analysis. This paper presents the required accuracy of converter reliability modeling for power system analysis in different applications.

4) The converter failure rate will be increased due to the aging of components. Thereby, they must be replaced according to a suitable maintenance strategy. The impact of run-to-fail and age replacement policies on the power system reliability is presented in this paper. In order to achieve the above-mentioned goals, Section II presents the concept of reliability in power electronics and power systems and their correlations. Section III represents the reliability modeling in power electronic converters. The reliability evaluation in power systems and incorporation of converter reliability in power system analysis are presented in Section IV. Numerical analyses are provided in Section V. Finally, the outcomes are discussed and summarized in Sections VI and VII.

II. C

ONCEPT OF

R

ELIABILITY

Reliability is defined as the ability of a system or an item to function under a desired conditions within a specific period of time [43], [44]. According to this definition, the system/item performance must be retained within a specified interval at a target time period. Depending on a system, the reliability measures may be different. For instance, in a mission-based system, such as a spacecraft, the reliability is defined as the probability of survival during the target mission period. Thus, the first time to failure with a desired probability must be longer than the target mission period. Furthermore, in a maintainable /repairable system/item with the possibility of maintenance, the performance is measured by the availability as its reliability indicator. In these systems/items, it is important to have them in the operation state (being available) at any instance regardless of any failure occurrence before that time [44]. This means that the system can be maintained whenever it fails and hence the only issues are the failure frequency and downtime.

A power system as a complex combination of large number of sub-systems and components should operate all the time for a long period of time. According to this expression, the power system performance, that is to supply its demand, must be guaranteed at all times. The short-term performance of a power systems is associated with the operation phase, which is defined as its ability to withstand any contingencies and outages. This ability is defined as security, that is related to the stability of power systems [45]. Moreover, power system long-term performance is associated with its ability to supply the load considering the uncertainty in generation availability and load level. This requires having adequate generation, transmission and distribution facilities. This ability is known as power system adequacy, which is a measure used for design and planning (facility and/or operational planning) [45]. As a result, the power system reliability is defined as its ability to supply the demand in a short-term by responding the contingencies and in a long-term by installing and employing adequate facilities. According to this definition, the facilities must have an accept-able level of availability to guarantee system performance.

One of the important measures of power system performance is loss of load/energy. The loss of load can be measured by different indices such as Loss Of Load Probability (LOLP), Loss Of Load Expectation (LOLE), Expected Energy Not Supplied (EENS) and so on [30], [44], [46], [47]. As a result, the power system reliability can be measured by loss of load indices. For instance, a reliable power system may have

LOLE from 4 to 8 hours per year [47]. A system with a higher value of LOLE is known as unreliable system. Based on this definition, the failure of one or more components might or might not affect the power system reliability. In order to achieve a reliable power system, the components and sub-systems must be maintained or replaced to improve their availability whenever it is required. Therefore, the availability of compon-ents is one of the main reliability indicators in power systems. In the modern power systems, power electronic converters are one the vulnerable components, which are also prone to wear-out failures [3]–[5], [12], [13]. Aging of converters will affect the overall system reliability since the higher failure rate will introduce lower availability. Therefore, reliability model-ing in power electronic converters as an underpinnmodel-ing technology of future power grids [1] is of paramount import-ance. The wear-out related reliability of converters depends on its aging-prone components such as capacitors and power modules. The reliability of these components is defined as the probability of survival within a target operating time. The failure rate of components can be thus found by failure probability function F(t). This failure probability function depends on the operating conditions and lifetime model of devices, where the lifetime of power modules is related to the number of cycles to failure Nf and lifetime of capacitors is

associated with the time to failure Lo [48].

Therefore, the reliability of power electronic based power systems can be modeled in three levels as shown in Fig. 1 [14]. In the component level, the lifetime model of component is employed to predict their failure rate by wear-our failure modeling under given operating and climate conditions. Then, the failure rate of components is used to model the converter reliability and failure rate based on the functionality of different components in the sub-system level. Afterwards, the converters availability is predicted according to the maintenance strate-gies. The availability of converters is incorporated into the power system reliability analysis to predict the system reli-ability indices such as LOLE and EENS. Moreover, according to the overall system reliability, proper maintenance times can be scheduled to obtain a desired level of reliability. This procedure is comprehensively explained in the following sect-ions for a power electronic based power system. It is exempli-fied for a wind-based renewable energy generation system.

Lifetime model (Nf, Lo, ...) Failure probability and

failure rate (F, λ, ...) System reliability (LOLE, EENS, ...) Availability _Ma in ten an ce Other subsystems Other components Wear-out modeling

Fig. 1. Correlation between power electronics and power system reliability concepts.

III. C

ONVERTER

R

ELIABILITY

M

ODELING

The failure characteristics of a converter, like other systems, comprises three periods including infant mortality, useful lifetime and wear-out phase as shown in Fig. 2 known as bathtub curve. Usually, the infant mortality failures are related to the debugging and manufacturing processes. Hence, the converter will experience the random chance and wear-out failures within operation. The random chance failures usually have external sources such as overcurrent, overvoltage and so on [48]. Therefore, they are considered as exponentially distributed failures within useful lifetime in the bathtub curve [48]–[50]. The corresponding failure rate is usually predicted based on the historical reliability data and operational experiences. Moreover, the wear-out failure rate is associated with the aging and degradation of device materials over a long-term operation and they are modeled by SSA over the aging prone components.

Following field data, the power modules (i.e., semiconductor devices) and capacitors are the most fragile converter components. The lifetime model of the electrolytic capacitors is obtained by [51]: 2 n o 1 n T T n o o n n V L L 2 V − −   =  _{ }  

,

(1)

where, Ln is the nominal lifetime under nominal voltage Vn and

upper category temperature Tn, and Lo is the capacitor lifetime

under operating voltage Vo and temperature To. The exponents

of n1 and n2 are obtained by lifetime testing [51]. Furthermore,

the number of cycles to failure, Nf in semiconductor devices is

calculated by using [52]: 0.3 on f j j t N A T exp T 1.5 





−     =   _{  } _      

,

(2)

where, ΔT and T are the junction temperature swing and its average value, and ton denotes the rise time of temperature

cycle. The constants of A, α, and β are curve fitting constants obtained from aging tests [52]. Notably, the junction temperature depends on the thermal loss of device, its thermal impedance and ambient temperature. Moreover, the thermal loss comprises two terms of conduction loss and switching loss [53], where the conduction loss is associated with the device current, voltage, on-state resistance. Furthermore, the switching loss depends on switching frequency and on-off energy loss. In order to obtain the lifetime of the devices, the annual mission profile should be translated to thermal variables in (1) and (2), i.e., temperature, and voltage, through electro-thermal analysis. This procedure is shown in Fig. 3(a). Therefore, the detailed electrical and thermal model of converter components must be employed which requires time-domain analysis.

Fa ilu re r a te Infant mortality Wear-out phase Time Useful Lifetime (Random Chance) Early wear-out

Cycle Counting Monte-Carlo Analysis Failure Distribution RSW(Diode)(t) To (c) ADs= DS-h DS,h=ncycle-h /Nf-h Switch (b) Tref

Time domain simulation

Tref Tj-SW(Diode) To El e ct ro -t h e rma l D o ma in Mo d e lin g Mission profile Cth,Cap, Rth,Cap Cth1,SW, Rth1,SW CthN,SW, RthN,SW Ploss Ploss Fragile components (a) Capacitor Vo Converter Control AD(Bx) = tk/Lo-k Bx lifetime Failure Distribution Diode Thermal domain simulation

Lo=Lr 2 n (Vo/Vr)-n To-Tt 1 2 Nf,h=AΔTj,hexp( )( )-0.3 α β Tjm,h ton 1.5 Monte-Carlo Analysis

RCap(t) λw-Cap(t) λw-SW(Diode)(t)

Tj-SW(Diode)

Fig. 3. Wear-out failure rate prediction in power converters, (a) electro-thermal mapping, (b) wear-out failure rate of capacitors and (c) wear-out failure rate of

semiconductor devices.

Following Fig. 3(a), the reliability prediction procedure consists two stages, where the first stage is in charge of electro-thermal modeling, and the second stage is associated with the reliability modeling. The first stage comprises two different domains of electrical and thermal domains, where the annual mission profile (which can be solar irradiance, wind speed, ambient temperature and so on) is translated into the electrical variables such as device voltage and current profile and then thermal variables such as junction and hotspot temperature. This process requires electrical modeling with the dynamics of switching frequency (several kilohertz to several ten kilohertz depending the converter capacity) over the whole mission profile with different power levels. Moreover, the lifetime of power devices depends on the junction temperature swing which is affected by the variation in the converter loading power and the thermal impedance of device. The thermal impedance is usually modeled by a higher order (3 to 5 order) transfer function as shown in Fig. 3(a). In order to translate the mission profile variation into the junction temperature swing, which remarkably affects the switch lifetime according to (2), a detail electro-thermal mapping is required. The complexity and calculation burden will be induced by solving differential equation of thermal model for long-term mission profile to obtain the temperature variations.

After translating the mission profile into the thermal variables, the thermo-mechanical damage of the devices must be calculated to predict the converter lifetime. Accumulated Damage of the Capacitors (ADCap) under a given mission profile

is obtained as: k Cap k o k t AD L₋ =



,

(3)

where, tk is the period that the capacitor operates under (Vo, To),

and Lo-k is the corresponding lifetime obtained by (1).

Moreover, in order to obtain the Accumulated Damage of Semiconductor devices (ADS), the junction temperature profile

is classified into different classes, where the class h is defined as a set of variables (Th, ΔTh, ton-h, ncycle-h). The ADs is then

obtained as: cycle h S h f h n AD N − − =



(4)

where, ncycle-h is the number of cycles in class h and Nf-h is the

corresponding number of cycles. The device lifetime is equal to the reciprocal of the AD in (3) and (4). The obtained AD values for each devices are associated with the specific values of lifetime models in (1) and (2) as well as specific thermal models of devices. In practice, the lifetime models and device thermal characteristics have uncertainties with a certain range of variations. Therefore, the distribution of AD in terms of model and manufacturing uncertainties must be identified. The AD distribution function can be obtained by Monte-Carlo simulations as shown in Fig. 3 (b & c). Notably, reflecting employing Monte Carlo simulations for reliability modeling will be also a time-consuming process. The reciprocal of the AD distribution function is known as the device unreliability function, F(t). Once, the unreliability function is obtained, the wear-out failure rate of components can be calculated as:

( )

1

_{( )}

( )

1 w X d t F t F t dt  − = −

,

(5)

where, d/dt is the differential operator and λw-X denotes as the

wear-out failure of device X. Usually, the wear-out failure rate is modeled by a Weibull distribution function with a hazard function of h(t) as:

( )

( )

1

w X

h t = ₋ t =− t −

,

(6)

where, α and β are the scale and shape factors of Weibull distribution. Finally, the device X failure rate λX is obtained by

using:

( )

( )

X t w X t c X

 =₋ +₋

,

(7)

where, λc-X denotes as the constant failure rate within useful

lifetime, which can be predicted based on historical failure data and operational experiences.

IV. P

OWER

S

YSTEM

R

ELIABILITY

Power system reliability, so-called adequacy is a measure of its ability to meet the electric power and energy requirements of the customers within acceptable technical limits considering the component outages [54]. The main measure employed in power system reliability assessment is the availability of its components. Availability is defined as the probability that an item is in operating state at any instant t given that it started to operate at instant zero. This section will present the general concept of components availability with time-constant and time-varying failure rates. Moreover, the reliability of power systems and its sub-systems will be presented.

A. Concept of Availability

Generally, the failure rate of components is considered constant (see Fig. 2) owing to the fact that they are regularly

maintained and the wear-out rarely happens. It is worth to mention that a run-to-fail replacement strategy is employed for availability prediction in this paper. For exponentially distributed systems, the availability can be obtained by using the Markov Process (MP). Following MP, system states can be represented as being in operating state of “1” and being in down state “2” as shown in Fig. 4(a). The system availability, A according to the MP is the probability of being in state “1”, which is obtained as [44]: 1 A FOR    = − = +

(8)

where λ, μ are the failure and repair rates within useful lifetime respectively. Forced Outage Rate (FOR) is defined as the unavailability following (8).

For the systems with non-exponential failures, the MP cannot be utilized. In this case, the failure rate can be decoupled into constant and time-varying terms. The cause of random chance failures in converter components such as capacitors and semiconductor devices are induced by abnormal operation and sudden over-stressing the components, while the wear-out failures are due to the long-term degradation of the component materials. Therefore, they have independent failure causes, and decoupling the failure rate into constant and time-varying terms is an appropriate assumption. As a result, a system with non-constant failure rate shown in Fig. 4(b) can be converted into two sub-systems with time-constant failure rate shown in Fig. 4(c) and time-varying term as shown in Fig. 4(d). According to Fig. 4(c & d), the system is available if and only if both sub-systems are available. Therefore, the total availability At(t) can

be obtained as:

A tt

( )

=A A tc w

( )

,

(9)

where, Ac(t) is associated with the time-constant failure rate

obtained by using (8). Moreover, the Aw(t) is related to the

time-varying failure rate with the Cumulative Distribution Function (CDF) of F12(t). In order to obtain the time-varying availability,

the Semi-Markov Process (SMP) can be employed [55], [56]. According to SMP, The probability of being in state j if the process starts at state i, ζij can be obtained by using (10) [55].

( )

(

( )

)

2

( )

(

)

1 0 1 t ij ij ij ik kj k k i d t F t F t d d        =  = − +



 −

,

(10)

where δij is:

(b) (a) λ Wear out 2 1 μ Success 2 1 λw(t) 2 1 μ λc 2 1 μ μ λ(t) Unit with constant failure rate Unit with non-constant failure rate

Decomposition into two sub-units with constant and

non-constant failure rates

λ(t) = λc+ λw(t)

Fig. 4. State space modeling of a single unit; (a) Markov model used for analyzing a unit with constant failure rate λ, (b) General model with non-constant failure rate λ(t) which is decomposed into two sub-units with time-constant failure rate λc, and with time-varying failure rate λw. The unit success

will be achieved if and only if both sub-units stay at operating state of “1”.

1 0 ij i j i j  =  =_ 

.

(11)

Following Fig. 4(d), F12(t) is the failure CDF and F21(t) is the

repair CDF with constant repair rate of μ. According to (10), the availability of the sub-system with time-varying failure rate is equal to the probability of being in state “1” given that the process has been started to operate in state “1”, hence,

A tw

( )

=11

( )

t

.

(12)

B. Availability of power converters

The reliability of a converter can be modeled by its components reliability as shown in Fig. 5(a). Since switches and capacitors are prone to wear-out failures [2], [57], their availability is modeled individually by using (9). The converter is available if, and only if, all the components are available as shown in Fig. 5(b). Hence, the overall converter availability is obtained by using (13).

( )

( )

( )

con SW Cap OC

A t =A t A t A

,

(13)

where, Acon(t), ASW(t), ACap(t) and AOC are the instantaneous

availability of power switch (SW), capacitor (Cap) and Other Components (OC). ASW(t) and ACap(t) are predicted by SMP

using (9) and AOC is predicted by MP using (8). C. Availability of HVDC system

The HVDC system contains a sending end converter, a receiving end converter and a DC transmission line. The HVDC system reliability can be modeled as a series network of these components as shown in Fig. 6. Hence, the availability of the HVDC system, AHVDC(t) is calculated as:

( )

( )

( )

HVDC con s con r DC

A t =A , t A , t A

(14)

where Acon,s(t) Acon,r(t) are the availability of the sending and

receiving end HVDC Converters (HC) obtained by using (13) and ADC is the availability of DC line obtained by using (8).

Power

Switch Capacitor Other Com.

(b) (a) Converter λOC μCap Switch (SW) 2 1 2 1 2 1

Capacitor (Cap) Other Comp. (OC)

μSW λSW(t) = λw-SW(t) + λc-SW λCap(t) μOC Success λSW(t)

λCap(t) = λw-Cap(t) + λc-Cap

Fig. 5. Power converter availability model; (a) availability block diagram, (b) Markov model. A converter success will be achieved if and only if all its

components are in operating state “1”.

Sending end

Converter Transmission Line

Receiving end Converter

HVDC System

D. Availability of wind turbine

A WT consists of different components such as blades, hub, generator, gear-box, converter, control [36]. Similar to the HVDC system, the availability of the WT, AWT(t) can be

obtained as:

( )

( )

WT con OC

A t =A t A

(15)

where, Acon(t) and AOC denote the availability of WT Converter

(WTC) and other components. Due to the uncertainty in wind power, its availability should also be included in the WT availability. One approach to model the wind power availability is to discretize the output power of the WT into some states. For instance, in a 2 MW WT, its output power can be divided into 0, 0.5, 1, 1.5, 2 MW as shown in Fig. 7. The probability of each state can be obtained by convolving the probability of wind power probability distribution with the WT characteristic curve [32], [35], [58]. Each state is available if the turbine is available. The availability of a 40 MW WF with twenty WTs can be obtained by combining the availability model of individual WT. Hence, the entire states will be 40, 39.5, 39, …, 0 MW. Therefore, like the conventional generation system [30], the capacity outage probability can be calculated for the WF. The detail analysis has been discussed in [32], [35]. According to Fig. 10, the wind power is available in the grid side if, and only if, the HVDC transmission line, i.e., WF Converters (WFCs) and DC line is available. Therefore, the total probability of each state must be convolved with the availability of WF HVDC line.

E. Reliability of wind farm

The performance of a WF can be measured by its availability [59]–[61]. Two kinds of availability measures can be defined for WFs including time-based availability Atime [59]

and production-based availability Aprod [60]. The annual

time-based availability is obtained by:

 

8760 1

time

Unavailable time

A h y

Available time Unavailable time

 

= _ − _

+

 

(16)

Time-based unavailability is the complementary of the time-based availability. Moreover, the production-time-based availability is calculated as:

1

prod

Lost production A

Actual energy production+ Lost production

= −

(17)

Furthermore, the reliability of a generation system, here a WF, can be measured by the Expected Energy Not Produced (EENP) due to the unavailability of WF components [62] as:

0MW 0.5MW 1MW 1.5MW 2MW 0MW 0.5MW 1MW 1.5MW 2MW W T UP AWT (t ) W T Do wn 1 -A WT (t ) 0 MW

Fig. 7. A 2 MW WT availability model – the highlighted states show zero generation due to either wind power unavailability or wind turbine

unavailability or both [32], [35], [37].

(

)

1 8760 n A u i i i i EENP  P P = =



 − 

(18)

where, Ψi is the WF capacity in state i, PiA is the probability of

state i considering the WF components are fully available and

Piu _{is the probability of state i considering the unavailability of}

the WF components.

F. Reliability of power system

Power system reliability is measured by probabilistic indices such as Loss Of Load Expectation (LOLE) and Expected Energy Not Supplied (EENS) [30], [46]. These two indices are the most popular measures of power system adequacy, where the LOLE is the number of days or hours within a specific period of time in which the load cannot be supplied due to the generation shortage, and it is calculated as:

(

)

1 n i i i i LOLE P C L = =



 −

(19)

where Ci is the available capacity in interval i, Li is the

forecasted peak load, Pi is the portability of loss of load [30].

EENS is also defined as the curtailed energy due to the generation shortage and it is estimated by using (20) [63].

1 n i i i EENS P E = =





(20)

where Ei is the curtailed energy.

The flow of the reliability prediction in the power system is shown in Fig. 8. First, the wear-out failure rate of power converters of WT is predicted according on SSA under given mission profile for each WT. Afterwards, the WTC availability is estimated based on wear-out and random chance failure rates. Then, the availability of WT is estimated according to the availability of the WT components and wind power availability. The WF HVDC transmission line availability can also be predicted based on converters wear-out failure and historical data of random chance failures. Combining the availability of the WTs and the WF transmission line will result in WF reliability model and its availability. Furthermore, the HVDC transmission system availability can also be predicted based on the availability of transmission line reliability which is obtained by converters wear-out random chance failures. The availability of the conventional generators can also be modeled based on availability of individual units according to [30]. The overall generation system reliability model can be obtained by combining the reliability models of WFs, HVDC systems and conventional generators. Finally, the system reliability indices including LOLE and EENS are predicted by convolving the generation system reliability and the system load model.

V. N

UMERICAL

A

NALYSIS

In the modern power systems, the energy sources can be conventional generators, Wind Turbines (WTs), solar photovoltaic arrays, energy storage systems, and neighboring grids. In this paper, the reliability of two power system structures is evaluated. The first system is the modified RBTS with additional 40 MW and 4×40 MW WFs with 20% and 64% wind penetration respectively. The structure of the modified RBTS is shown in Fig. 9. The RBTS information including reliability data and load model are provided in [64]. The structure of the 40 MW WF is shown in Fig. 10 including twenty 2 MW V80-2.0 WTs manufactured by Vestas Wind

Systems with cut-in, rated, and cut-out speeds of 4, 15, and 25 m/s, respectively. The WF is connected to the grid through a DC transmission line. Wind speed data of two different location with resolution of one minute is utilized as shown in Fig. 11.

Moving toward one hundred percent renewable energies necessitates the power systems to interconnect into the neighboring grids. Therefore, the RBTS is further modified by interconnecting to the neighboring grids through three 100 MW HVDC lines as shown in Fig. 12. The modified RBTS is fully equipped with Power Electronics (PE), and it would be called modified PE-RBTS. In this case, it is assumed that the neighboring grids are always available and the local grid does not support the neighboring grids. In the following, the reliability of the two power systems is analyzed.

LDC Time Po w e r WT Reliability model WT generation model Generation system model Wind power uncertainty model WF generation model Generators model Convolving generation and load models Load profile Generators Reli. Data Mission profile EENP Atime Aprod LOLE EENS HVDC System model Reliability Data Converter Reliability Model Converter Reliability Model Mission profile Reliability Data Reliability Data Line Converter Reliability Model Mission profile Reliability Data ACon ACon ACon AHVDC AWT Agen AWF

Fig. 8. Reliability evaluation in modern power systems.

N×40 MW 2 3 4 5 6 1 G G Wind Farm 40 MW AC DC Generator Load G 20x2 MW

Fig. 9. Modified RBTS (The main version is provided in [64]), Wind Farm Converter (WFC). AC DC Wind Farm 40 MW Grid WFC WT 1 WFC WT 20 WTC WTC WF HVDC Line

Fig. 10. A 40 MW DFIG based Wind Farm (WF) Structure with 20×2 MW Wind Turbines (WTs). W in d sp e e d ( m /s) Ja n W in d sp e e d ( m /s) 0 5 10 15 Fe b M a r A p r M a y Ju n Ju l A u g S e p O ct N o v D e c Ja n Ja n F e b M a r A p r M a y Ju n Ju l A u g S e p O ct N o v D e c Ja n Location A Location B 20 0 5 10 15 20

Fig. 11. Wind speed profile of two locations with one-minute resolution.

2 3 4 5 6 HVDC 3 HVDC 2 1 Neighboring grid Neighboring grid HVDC 1 Neighboring grid HC HC HC HC HC HC N×40 MW Wind Farm 40 MW 20x2 MW AC DC Load

Fig. 12. Full Power Electronic based RBTS (PE-RBTS). HC: HVDC Converter.

A. Converter availability

The converter availability (or unavailability) depends on the random chance and wear-out failure rates. The random chance failure rate of converters is provided in Table APP-I in Appendix. Moreover, the wear-out failure rate is predicted based on SSA for the WT converter shown in Fig. 10 under the given mission profiles in Fig. 11. The converter structure and characteristics for a 2 MW DFIG-based WT is provided in [65] which includes a 0.4 MW partial-scale two-level converter. Since the thermal modeling and SSA of converters have been widely addressed in [18], [22], [48], [65], [66], the detail modeling process is not represented here. Hence, the reliability prediction is carried out following the procedure described in Fig. 3, and the results are employed for system-level analysis.

The wear-out failure rates are represented by a Weibull distribution as given in (6). Following SSA-based reliability prediction approach, the wear-out failure rate characteristics of the converter switches and capacitors are obtained as (α, β)switch

= (12, 3), (α, β)cap = (10, 3) for mission profile of location A and

(α, β)switch = (8, 3), (α, β)cap = (7, 2.6) for location B.

The converter components unavailability is predicted for both constant and time-varying failure rates using (9). Their unavailability due to the random chance failures and the total unavailability are shown in Fig. 13. The total converter unavailability due to the random chance failures is almost 0.007. It can be seen from Fig. 13 that the wear-out of converter components will increase its unavailability from 0.007 to 0.011. shape factors (α, β). As a result, employing the random chance failure rate, and neglecting the impact of components aging will introduce error on the converter reliability. The unavailability of the HVDC converters of WF and transmission systems in the modified RBTS test systems can be predicted similar to this case, and the total unavailability can be used for system-level analysis.

B. Wind farm reliability

The WF reliability is evaluated employing the historical reliability data summarized in Table APP-I as a base case. These data are associated with the random chance failures. For the base case, the reliability indices are summarized in TABLE I, where the time-based unavailability is 168 h/y, the production-based availability is 97.0 % and the EENP is equal to 1,8550 MWh/y.

The impact of converter components wear-out on the performance of the 4×40 MW WF is illustrated in Fig. 14. The wear-out characteristics of WTC under two mission profiles is (α, β)switch = (12, 3), (α, β)cap = (10, 3) for location A and (α,

β)switch = (8, 3), (α, β)cap = (7, 2.6) for location B. Moreover, for

the WFC, the components wear-out characteristics is assumed to be (α, β)switch = (α, β)cap = (12, 3), and (α, β)switch = (α, β)cap =

(8, 3) respectively for location A and B. According to Fig. 14(a) and (b), the impact of WTC on the time-based unavailability and production-based availability is negligible. Also, the impact of WFC on the time-based unavailability is 74 h/y higher than the base case (168 h/y) in Location B as shown in Fig. 14(a). Therefore, ignoring the impact of WFC and using the historical reliability data will introduce almost 44 % error in time-based unavailability prediction following Fig. 14(a).

Without aging With aging Switch total Capacitor Other components

Fig. 13. Impact of component aging on the converter unavailability, U(t); (α,

β)switch = (12, 3), (α, β)cap = (10, 3). TABLE I

Wind Farm (WF) reliability indices for the base case given in the Appendix.

WF Time-U

[h/y] Prod-A [%] EENP [MWh/y]

160 MW 168 97 18,550

Furthermore, as it is shown in Fig. 14(a), the aging parameters of the WFC can affect the unavailability of the WF, where by decreasing α from 12 in location A to 8 in location B, the maximum time-based unavailability is increased from 218

h/y to 242 h/y. The EENP of the WF is illustrated in Fig. 14(c)

highlighting the impact of converters wear-out. The aging of WTC will introduce 1,940 MWh/y EENP over the base case which is almost 10%. Furthermore, wear-out of WTCs and WFCs causes 5,080 MWh/y in location A and 7,660 MWh/y in location B more EENP compared to the base case, which are equal to 27% and 41% of the base case, respectively.

The results in Fig. 14 show that the different WF availability measures are not identical, and may not appropriately show the WF performance. For instance, the impact of WTC wear-out on the time-based unavailability is almost negligible while it can introduce 10% more EENP over the base case. Furthermore, the aging parameters of WTCs and WFCs can affect the reliability of the WF, and thus, need to be modeled in system-level analysis. However, the impact of WFC wear-out is much higher than the impact of WTC. This case study shows that the wind speed profile can affect the converters reliability, and hence, the WF availability. Thus, modeling the converters aging in system-level analysis is of high importance.

Since the converter failure rate is dependent on the operational and environmental conditions, a senility analysis is performed to show the impact of random chance failure rates on the overall performance of WF. Notably, during the sensitivity analysis on the FOR of one of the WTC or WFC, the FOR of the other one is kept constant at the base case as given in Table APP-I. Following Fig. 15(a), the FOR of WTC does not affect the time-based unavailability and its impact on the production-based availability is almost negligible as shown in Fig. 15(b). Meanwhile, the WFC considerably affect the time-based unavailability and production-time-based unavailability of the WF reliability as shown in Fig. 15.

(a) (b) (c) Location A Location B WTC & WFC WTC 74 50 7660 5080 1940 WTC WTC WTC & WFC WTC & WFC Uti m e [h /y] Ap ro d [h /y] E E NP [M W h /y]

Fig. 14. Impact of WTC and WFC wear out on the reliability of 160 MW WF, (a) Time-based unavailability, (b) production-based availability, (c) EENP due

(a) (b) WTC WFC WTCWFC Ap ro d [h /y ] Uti m e [h /y ] FOR [%] FOR [%]

Fig. 15. Impact of WTC and WFC unavailability (FOR) on the (a) time-based unavailability and (b) production-based availability of the WF.

(a) (b) WTC WFC WTC WFC FOR [%] FOR [%] E E N P [ M W h /y ] E E N P [ M W h /y ]

Fig. 16. Impact of WTC and WFC unavailability (FOR) on the EENP by the (a) 40 MW and (b) 160 MW WF.

Furthermore, the EENP of a 40 MW and 4×40 MW WFs are calculated for the base case which is equal to 4.64 and 18.55

GWh/y respectively. The impact of converters FOR is reported

in Fig. 16(a) and (b) respectively. The results show that increasing the WFC FOR remarkably increases the WF EENP, while the impact of WTC on the EENP is not considerable.

C. Power System Reliability

The reliability of modified RBTS and PE-RBTS is evaluated by LOLE and EENS indices. The base case reliability indices are summarized in TABLE II. The LOLE of the RBTS is 1.14

h/y. In order to approximately keep the LOLE to be identical to

the base case, the peak load of the system is increased accordingly. This incremental peak load, which is called Peak Load Carrying Capability (PLCC), for modified RBTS is reported in TABLE II. Furthermore, the PLCC for the EP-RBTS is considered as the case of EP-RBTS with 160 MW WF, since the wind capacity penetration in both cases is identical.

C.1. Modified RBTS reliability

The impact of WTC and WFC wear-out failure on the system reliability is illustrated in Fig. 17 with the 160 MW WF. First, the aging of WTCs is considered. Following Fig. 17, the WTCs wear-out has negligible impact on the system LOLE and EENS. Next, the aging of both WTCs and WFC is modeled. The obtained results in Fig. 17 shows that the converters aging impact on the LOLE is 2% and EENS is 3%. As a result, for power system-level analysis, the WTCs and WFCs wear-out failure impacts can be neglected.

TABLE II

Reliability indices of power system for the base case given in the Appendix.

SYSTEM RBTS PE-RBTS WF Capacity [MW] 0 40 160 160 PLCC [MW] 0 16 65 65 Peak load [MW] 185 201 250 250 Wind penetration [%] 0 20 64 64 LOLE [h/y] 1.14 1.24 1.31 4.10 EENS [MWh/y] 10.00 9.57 12.48 165.00 (a) (b) 0.35 WTC WTC & WFC WTC & WFC WTC Location A Location B

Fig. 17. Impact of WTC and WFC wear out on the reliability of RBTS with 160 MW WF, (a) LOLE, (b) EENS.

(a) (b) WTC WFC WTC WFC 160 MW 40 MW 160 MW 40 MW

Fig. 18. Impact of WTC and line converter unavailability (FOR) on the (a) LOLE and (b) EENS in RBTS with 40 MW and 160 MW WF. Moreover, the impact of WTCs and WFCs FOR on the RBTS reliability is shown in Fig. 18(a) and (b) with the 40 and 160 MW WFs. The sensitivity analysis is performed on the FOR of one of the WTC or WFC, while the FOR of the other one is assumed to be constant as given in Table APP-I. As it can be seen in Fig. 18, increasing the WTC FOR cannot affect the LOLE and EENS with low and high penetration of wind power. However, the system reliability is dependent on the WFC FOR and wind power penetration. As it can be seen in Fig. 18(a), by increasing the WFC FOR with 40 MW WF, the change of LOLE is almost negligible. However, with the 160 MW WF, the impact of WFC FOR on the LOLE is significant as shown in Fig. 18(a). The impact of FOR of converters on the EENS is also similar to the LOLE as shown in Fig. 18(b). Therefore, the WTCs impact on the system reliability is almost negligible, while the WFCs can affect the system reliability especially with high wind power penetration. Thus, the appropriate reliability data of WFCs should be employed in the system-level reliability assessment.

C.2. Modified PE-RBTS reliability

The reliability of the full power electronic-based system, PE-RBTS shown in Fig. 12 is evaluated in this sub-section. The base case reliability indices have been summarized in TABLE II. Following these results, replacing the conventional generators with HVDC systems connected to the neighboring grids, the base LOLE is increased from 1.31 to 4.10 h/y. Moreover, the system EENS is increased from 12.38 to 165.00

MWh/y. Therefore, moving to full power electronic systems

requires HVDC systems with high availability in order to obtain the same performance as the conventional systems.

In order to illustrate the impact of HC aging on the system reliability, the wear-out characteristics of HC converter components are assumed to be (α, β)switch = (α, β)cap = (8, 3).

The PE-RBTS LOLE and EENS due to the wear-out failure of WFCs and HCs are shown in Fig. 19. The HCs aging increases the LOLE by 4.5 h/y (109%) and EENS by 190 MWh/y (115%) as shown in Fig. 19(a) and (b). However, the WFCs wear-out impact on LOLE and EENS is negligible.

Moreover, the impact of FOR of HCs and WFCs with 160 MW WF with wind capacity penetration of 65% is shown in Fig. 20. As it can be seen from Fig. 20, the LOLE and EENS are significantly affected by the HC FOR, while the impact of WFCs is negligible. Notably, the WFC FOR is kept constant as given in the Table APP-I within analyzing the impact of HC FOR and vice versa. The obtained results show that the random-chance and wear-out failure rate of HC components have significant impact on the overall system reliability.

Therefore, in a full power electronic based power system, accurate reliability analysis requires utilizing appropriate reliability data for random chance failures must be utilized. Moreover, the detailed wear-out failure rate of HC components must be predicted in order to accurately analyze the system reliability. Ignoring the aging of components may introduce erroneous results, consequently non-optimal decision-making within planning and operation of such systems.

C.3. Impact of replacement policy

The LOLE index in a reliable power system must be limited to a standard value, which depends on every country’s regulations. For instance, its standard value for European countries is between 4 and 8 h/y [47]. Considering the standard level of 6 h/y, the system performance with the run-to-fail maintenance strategy is not acceptable as shown in Fig. 19(a). Therefore, a proper maintenance strategy such as an age replacement policy must be adopted in order to maintain the system reliability. According to the age replacement policy, the components will be replaced upon failure or specific time to,

whichever comes first. Following the system performance shown in Fig. 19(a), the appropriate time of replacement based on the age replacement policy would be the cross points of LOLE cures with the standard level of 6 h/y. As it can be seen from Fig. 19(a), the appropriate planned replacement time to,

would be 4 years. As a result, applying the age replacement policy at the planned times, the overall system reliability can be obtained as shown in Fig. 21. It is clear that the time of planned replacement scheduling depends on the wear-out failure characteristics of the HC converters. Therefore, accurate wear-out failure prediction of converters is necessary for appropriate maintenance scheduling in modern power systems.

(a) (b) α = 8, β = 3 With aging of WFC Without aging of WFC 190 With aging of WFC Without aging of WFC 4.5 STD LOLE 6 h/y 4

Fig. 19. Impact of WFC and HC wear out on the reliability of FE-RBTS with 160 MW WF, (a) LOLE, (b) EENS.

(a) (b) WFC HC WFC HC FOR [%] FOR [%] L O L E [ h /y ] E E N S [ M W h /y ]

Fig. 20. Impact of WTC and WFC unavailability (FOR) on the (a) LOLE and (b) EENS in PE-RBTS with 40 MW and 160 MW WF.

(a)

(b) β = 3

t0 = 4

α = 8

Fig. 21. Impact of the age replacement policy of HC on the reliability of FE-RBTS with 160 MW WF, (a) LOLE, (b) EENS.

VI. D

ISCUSSION

The converters are utilized in generation systems such as for wind and solar energy resources, and electronic transmission systems such as HVDC lines. Hence, the converter reliability may affect the overall system reliability according to its applications. Meanwhile, the converters are fragile components and particularly they are prone to aging failures. Thereby, this paper has explored the impact of converter failures on the modern power electronic-based power systems performance. First, the wear-out failure prediction based on SSA in power converters has been presented. Next, the converter reliability model has been incorporated into the power system analysis. Finally, the reliability evaluation in modern power systems has been presented. The impact of converters reliability on the modified RBTS with different proliferation of power converters has been illustrated.

It has been shown that the wear-out failures can affect the converter availability according to the aging parameters. The impact of converter availability on the WF reliability has been illustrated with 20 and 64% wind power penetration. The obtained results have shown that the WTC has negligible impact on the time-based unavailability and production-based availability of WFs. However, its wear-out failure may increase the EENP by 10% compared to the case of neglecting the wear-out failures. Furthermore, the WFC can highly affect the WF reliability indices. The analysis has shown that the wear-out failure of WFC may introduce almost 45% unavailability over the base case. As a result, the WFC reliability considering the random chance and wear-out failures must accurately be modeled for reliability prediction of WFs. Since, the number of these converters are not too much, e.g., two converters per 40 MW WF, hence, its reliability modeling based on SSA might not be time consuming. However, the number of WTCs is quite

high, e.g., 2×40 converters in a 40 MW WF. Thereby, its reliability modeling especially considering different mission profiles for each WT in practice, is almost impossible. As a result, considering the time of analysis with high penetration of WFs, the wear-out reliability of WTCs can be neglected, while it can induce 10% error in the results.

The impact of WTCs and WFCs on the reliability of RBTS with 20% and 64% of wind power penetration has been evaluated. It has been shown that the impact of WTCs and WFCs failures including random chance and wear-out failures on the LOLE and EENS in low and high wind power penetration is almost negligible. Thus, the SSA-based wear-out analysis for the system-level studies for both WTCs and WFCs may not be necessary. However, the WFC FOR can affect the system reliability in high wind power penetration. Therefore, for system reliability analysis, the WFC FOR due to the random chance failures must be appropriately adopted from operation experiences and historical data.

Finally, a modified version of RBTS as a full power electronic system, PE-RBTS is considered with three HVDC links connected to the neighboring countries. The obtained results have shown that the reliability of the system significantly depends on the HVDC system availability. Furthermore, the wear-out failure of HCs has a remarkable impact on the overall system reliability. Therefore, the HC reliability, especially the wear-out failures, must be accurately modeled for the system-level analysis. Furthermore, the impact of run-to-fail and age replacement polices for HCs has been shown in this paper, where the age replacement policy at a proper time is required to maintain the system reliability under a standard limit.

This paper bridged the reliability concept of power electronic converters and power systems. It presented a method to model the reliability of power electronic based power systems from device level up to power system level. Moreover, the impact of power converters on the system reliability at different applications with different penetration level of renewable (wind) energies was illustrated. In the analysis, the wind profile for all WTs are considered to be identical. The impact of wind regime with different wind profile of WTs on the converter and WF and power system reliability will be analyzed in the future. Furthermore, the neighboring networks are assumed to be a back-up to support the grid security. The future work will be focus on the full renewable energy grids with energy storage systems, where all the energy sources are equipped with power electronic converters. Hence, the impact of long-term energy management system and storage system converter on overall system reliability should be explored.

VII.

C

ONCLUSION

This paper has proposed a procedure to bridge the power electronic and power system reliability concepts. The reliability of power electronic converters is incorporated in power system reliability analysis, which can be beneficial for optimal decision-making within planning, operation and maintenance of modern power systems. The detailed reliability modeling of power electronic-based power systems has been presented from device-level up to power system-level. The impact of converter failure rates on power system performance has been illustrated for different applications. For instance, it has been shown that

the wear-out failure of wind turbine converter cannot affect the wind farm and power system performance even under run-to-fail replacement strategy. Moreover, since, the converter reliability modeling in electro-thermal domains is a time-consuming process, the required accuracy in reliability modeling of power converters for different applications has been addressed. This can facilitate the system-level reliability evolution on modern power systems with high proliferation of power converters. Furthermore, the impact of run-to-fail and age replacement polices for power converters on the overall system reliability has been illustrated.

The reliability assessment approach can be easily performed for photovoltaic systems by appropriately modeling the availability of the solar energy. The remaining analysis will be similar to the wind power plants. Future research will focus on the impact of power management strategies on the system-level reliability of converters. Moreover, appropriate maintenance strategies could be introduced for different applications of converters in power systems.

VIII. A

PPENDIX

The reliability data for base case used in this paper are summarized in TABLE APP-I which are based on the data provided in [3], [36], [37], [67], [68].

TABLE APP-I

Exponential failure and repair rates of WT and HVDC system. Unit Sub-system Component Failure rate _[occ/y] Repair rate _[r/y]

WT Converter (con.) Switch 0.15 150 Capacitor 0.2 150 Other con. comp. 0.15 185

Other Other WT comp. 0.53 200

HVDC Converter (con.) Switch 0.3 200 Capacitor 0.43 50 Other con. comp. 0.35 10 Other Comp. DC Line 0.003 17

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